How to turn generated mapping to UV Map
The problem here is that UV unwrapping simply assigns U (X) and V (Y) coordinates to the mesh, the W (Z) coordinate remains at 0 across the entire mesh.  Generated coordinates are based on the 3-dimensional bounding box of the mesh.

However, you can recreate the U and V generated coordinates in a UV map.

Just go into top view (Numpad 7) and hit U > Project From View (Bounds).



This will result in the same U an V coordinates as generated mapping.

For more on texture coordinates see my explanation of texture coordinates here.